If Alice's age at death is correct, she was born about 1810. Unfortunately, recorded baptisms in Ireland become a bit thin on the ground before 1830.
The only Linskay (or variant) I can see at the moment - baptised around 1810 in Limerick, was a William Lynsky baptised 10 Dec 1815 in Mahoonagh/Castlemahon. Parents - Patrick Lynsky and Mary Costello.
It doesn't help much I'm afraid - maybe one of her sons was named Patrick? Mary is a rather common name to be evidence, if she named a daughter, Mary.